Proof of (b). By assumed conditions in (b) and Lemma REF (e), we have \( \rho (D)>1\) . Then using the similar procedures in the proof of (a), we can obtain that \( \rho (C^{(m)}) \rightarrow _p \rho ^M(D) > 1\)  as \( n\rightarrow \infty \) . Consequently, \( \lbrace C^{(m)}\rbrace ^t \lnot \rightarrow 0\)  as \( t\rightarrow \infty \)  holds with probability tending to one as \( n \rightarrow \infty \)  [1]}. Thus, as long as \(\delta ^{(0, m)}\ne 0 \) , \( \delta ^{(t, m)} \)  will not converge to zero with probability tending to one as \( n \rightarrow \infty \) . We have proved (b) and complete the proof.
